Difficulty: Intermediate | Prerequisites: time value of money, basic CAPM (Ch. 9), fixed-income pricing concepts.
Equity valuation answers the question every investor faces: what is a stock worth? This chapter introduces the dividend discount model and its variants, connecting a stock's price to its expected future dividends, its growth rate, and the investor's required return. It also bridges CAPM (which gives you the required return) to the valuation models (which use that return to discount cash flows). If you are comfortable pricing bonds, you already have the PV intuition; the new piece is modelling a stream of growing cash flows that has no fixed end date.
TL;DR
A stock's value is the present value of its expected future dividends. The Gordon growth model prices a stock as D1 / (k - g), where D1 is next year's dividend, k is the required return, and g is the constant growth rate. Growth comes from retained earnings reinvested at the firm's ROE.
Dividend yield
Expected dividend divided by current market price: D1 / P0. It measures the income component of a stock's return.
Capital gains yield (rate of price appreciation)
The expected percentage increase in the stock's price over the holding period: (P1 - P0) / P0.
Holding-period return (HPR)
The total return from holding a stock for one period: dividend yield plus capital gains yield. HPR = (D1 + P1 - P0) / P0.
In simple terms: everything you earn (dividends plus price change) divided by what you paid.
Required rate of return (k)
The minimum return an investor demands for bearing the stock's risk. Determined by the CAPM: k = r_f + β(E[r_m] - r_f).
Intrinsic value (V0)
The "true" value of a stock based on its fundamentals, calculated as the present value of expected future cash flows discounted at the required rate. If V0 > P0, the stock is undervalued.
Gordon growth model (constant-growth DDM)
A special case of the dividend discount model that assumes dividends grow at a constant rate g forever. V0 = D1 / (k - g). Requires k > g.
Think of it as the workhorse formula for stock valuation when growth is steady and predictable.
Plowback ratio (b, retention ratio)
The fraction of earnings retained and reinvested in the firm rather than paid out as dividends. b = 1 - dividend payout ratio.
Return on equity (ROE)
The firm's net income divided by shareholders' equity. It measures how productively the firm uses its equity capital.
Sustainable growth rate (g)
g = b × ROE. The rate at which earnings and dividends can grow if the firm reinvests a fraction b of its earnings at a return of ROE.
In simple terms: how fast the firm can grow by ploughing profits back in.
Present value of growth opportunities (PVGO)
The portion of a stock's price attributable to its future investment opportunities, beyond what it would be worth as a no-growth firm. PVGO = P0 - E1/k.
Price-to-earnings ratio (P/E)
P0 / E1. It reflects the market's willingness to pay per dollar of earnings. A higher P/E suggests the market expects higher growth or lower risk, or both.
The expected HPR on a stock has two parts:
Dividend yield: D1 / P0
Capital gains yield: (P1 - P0) / P0
HPR = Dividend yield + Capital gains yield
Example: XYZ stock trades at $50, expected to pay $2.15 and reach $59.77 in a year.
Dividend yield = 2.15 / 50 = 4.30%
Capital gains yield = (59.77 - 50) / 50 = 19.54%
HPR = 4.30% + 19.54% = 23.84%
The CAPM links a stock's required return to its systematic risk:
k = r_f + β × (E[r_m] - r_f)
Example: risk-free rate 6%, market return 14%, beta 1.15.
k = 6% + 1.15 × (14% - 6%) = 6% + 9.2% = 15.2%
If the expected HPR (23.84%) exceeds the required return (15.2%), the stock looks undervalued.
Intrinsic value is what the stock should be worth given its expected cash flows and the required return:
V0 = (D1 + P1) / (1 + k)
Example: V0 = (2.15 + 59.77) / 1.152 = 61.92 / 1.152 = $53.75.
Since V0 ($53.75) > P0 ($50), the stock is undervalued. A rational investor would buy.
If dividends grow at a constant rate g forever, the stock's intrinsic value simplifies to:
V0 = D1 / (k - g)
This works because the infinite series of growing dividends collapses into this clean expression. The requirement is that k > g; otherwise the series diverges (the stock would have infinite value, which makes no sense).
Example: D1 = $2.15, g = 11.2%, k = 15.2%.
V0 = 2.15 / (0.152 - 0.112) = 2.15 / 0.04 = $53.75.
A key result: under the Gordon model, the stock's price grows at exactly the same rate as dividends, g. So if the stock is fairly priced today at $53.75, next year's expected price is:
P1 = V0 × (1 + g) = 53.75 × 1.112 = $59.77
This means the capital gains yield equals g, and the dividend yield equals k - g.
Dividend yield = D1/P0 = 2.15/53.75 = 4.0%
Capital gains yield = g = 11.2%
HPR = 4.0% + 11.2% = 15.2% = k
When a stock is fairly priced (P0 = V0), the expected HPR equals the required return. This is the equilibrium condition.
The sustainable growth rate comes from the plowback decision:
g = b × ROE
where b is the plowback (retention) ratio and ROE is return on equity.
A firm with b = 0.60 and ROE = 20% grows at 12%.
A firm with b = 0.60 and ROE = 10% grows at only 6%.
Retaining earnings only adds value if ROE exceeds the required return k. If ROE < k, the firm is reinvesting at a rate below what investors demand, and paying out more (lower b) would increase the stock price.
A firm's price can be decomposed into two parts:
P0 = E1/k + PVGO
The first term (E1/k) is what the firm would be worth if it paid out all earnings as dividends (a no-growth firm). PVGO is the additional value created by reinvesting earnings into positive-NPV projects.
Example: E1 = $5, k = 12.5%, b = 0.60, ROE = 20%. Then g = 0.60 × 20% = 12%, D1 = 5 × (1 - 0.60) = $2. Price = 2 / (0.125 - 0.12) = $400. The no-growth value = 5 / 0.125 = $40. PVGO = 400 - 40 = $360. Most of this firm's value comes from growth opportunities.
Now consider ROE = 10% (below k = 12.5%). g = 0.60 × 10% = 6%, D1 = $2. Price = 2 / (0.125 - 0.06) = $30.77. The no-growth value is still $40. PVGO = 30.77 - 40 = -$9.23. Negative PVGO: the firm is destroying value by reinvesting. It would be worth more ($40) if it stopped investing and paid everything out (b = 0).
P/E = P0 / E1 = (1 - b) / (k - g) = (1 - b) / (k - b × ROE)
The P/E ratio rises when:
The growth rate g increases (higher b or higher ROE, provided ROE > k)
The required return k decreases
The plowback ratio increases, but only if ROE > k
Example: E1 = $2, dividends = $1.50, ROE = 12%, k = 10%. Plowback b = 1 - (1.50/2) = 0.25. Growth g = 0.25 × 12% = 3%. Price = 1.50 / (0.10 - 0.03) = $21.43. P/E = 21.43 / 2 = 10.71.
If b rises to 0.40: D1 = 2 × 0.60 = $1.20, g = 0.40 × 12% = 4.8%, Price = 1.20 / (0.10 - 0.048) = $23.08. P/E = 23.08 / 2 = 11.54. Higher plowback raised the P/E because ROE (12%) exceeds k (10%).
\text{HPR} = \frac{D_1 + P_1 - P_0}{P_0}k = r_f + \beta (E[r_m] - r_f)V_0 = \frac{D_1 + P_1}{1 + k}V_0 = \frac{D_1}{k - g} \quad \text{(Gordon growth model, requires } k > g \text{)}g = b \times ROEP_0 = \frac{E_1}{k} + PVGO\frac{P_0}{E_1} = \frac{1 - b}{k - b \times ROE}"High growth always means a higher stock price." Growth adds value only if ROE > k. A firm growing quickly by reinvesting at a return below its cost of capital is destroying value. PVGO can be negative.
"A high P/E means the stock is overvalued." Not necessarily. A high P/E may simply reflect high expected growth, low required return, or both. You need to check whether the P/E is justified by fundamentals.
"The Gordon model works for any stock." It requires a constant, perpetual growth rate below the required return. It does not work for high-growth firms where g approaches or exceeds k, for firms with irregular dividend patterns, or for firms that do not pay dividends.
"Dividend yield and capital gains yield are independent." Under the Gordon model, they are linked: dividend yield = k - g and capital gains yield = g. They must sum to k in equilibrium.
⚠️ Decomposing HPR into dividend yield and capital gains yield is a very common exam question. Know the formulas cold.
⚠️ CAPM calculation for required return: plug in and solve. Do not confuse the market risk premium (E[r_m] - r_f) with the market return itself.
⚠️ The Gordon model V0 = D1/(k - g) appears on virtually every exam covering this chapter. Practice both forward (given D1, k, g, find V0) and backward (given V0 and two of the three, find the third).
⚠️ PVGO decomposition: be able to compute E1/k (no-growth value) and then PVGO = P0 - E1/k. Know how to interpret a negative PVGO.
⚠️ The plowback/ROE/growth connection (g = b × ROE) and its effect on P/E is a frequent exam topic. Be clear on when higher retention helps (ROE > k) vs hurts (ROE < k).
True or False: Under the Gordon model, the capital gains yield equals the dividend growth rate g. Answer: True.
Fill in the blank: PVGO is negative when ROE is ______ than k. Answer: Less (lower).
True or False: A stock with a beta of 1.0 has a required return equal to the risk-free rate. Answer: False. Its required return equals the market return (r_f + 1.0 × market risk premium = E[r_m]).
Fill in the blank: If V0 > P0, the stock is ______ and a rational investor would ______. Answer: Undervalued; buy.
True or False: Increasing the plowback ratio always increases a firm's stock price. Answer: False. Only if ROE > k.
Q: A stock trades at $50, is expected to pay a $2.15 dividend and reach $59.77 in one year. What is the HPR?
A: HPR = (2.15 + 59.77 - 50) / 50 = 11.92 / 50 = 23.84%.
Q: Using CAPM with r_f = 6%, beta = 1.15, E[r_m] = 14%, what is the required return on the stock?
A: k = 6% + 1.15 × 8% = 15.2%.
Q: A firm has D1 = $2.15, g = 11.2%, k = 15.2%. What is its intrinsic value under the Gordon model?
A: V0 = 2.15 / (0.152 - 0.112) = 2.15 / 0.04 = $53.75.
Q: E1 = $5, b = 0.60, ROE = 20%, k = 12.5%. What is the stock price, and what is PVGO?
A: g = 12%, D1 = $2. Price = 2 / (0.125 - 0.12) = $400. No-growth value = 5/0.125 = $40. PVGO = $360.
Q: Same firm but ROE = 10%. What happens to PVGO?
A: g = 6%, D1 = $2. Price = 2 / (0.125 - 0.06) = $30.77. PVGO = 30.77 - 40 = -$9.23. The firm destroys value by reinvesting. With b = 0, price would be $40.
The required return k from CAPM (Ch. 9) is the discount rate that plugs directly into the DDM. Without CAPM, you have no principled way to set k, so these chapters are tightly linked.
The present-value logic here is identical to bond pricing (Ch. 14-16), except that equities have uncertain, growing cash flows and no maturity date, while bonds have fixed cash flows and a known end point.
PVGO analysis connects to corporate finance: a firm's investment decisions (whether to retain and reinvest) show up directly in its stock price. This foreshadows capital budgeting and the NPV rule.
Related Terms / Search Tags
Dividend discount model, DDM, Gordon growth model, constant-growth model, dividend yield, capital gains yield, holding-period return, HPR, CAPM, required rate of return, intrinsic value, undervalued, overvalued, plowback ratio, retention ratio, payout ratio, ROE, return on equity, sustainable growth rate, PVGO, present value of growth opportunities, P/E ratio, price-to-earnings, no-growth firm, equity valuation, stock valuation, beta, risk-free rate, market risk premium